4 A certain lake is stocked with 1000 fish The population is

4) A certain lake is stocked with 1000 fish. The population is growing according to the logistics 000 10,000 curve: P- 10,0ed a) Find t 1 +es where tis a) Find the population in 8 months where t is measured in months since the lake was initially stocked. After how many months will the fish population be 2000? Use a graphing calculator, online application (Wolfram Alpha), or some other means to graph the equation. Is there a maximum possible fish population that the lake can sustain? What graphical feature is this on the graph? b) c) d)

Solution

a)P(t) = 10,000/[1 + 9e^(-t/5)]
When t = 8, P = 10,000/ [1 + 9e^(-8/5)] = 3549.79
b)2000=10,000/[1 + 9e^(-t/5)]

10000/2000=1+9e^(-t/5)
5=1+9e^(-t/5)
4/9=e^(-t/5)
ln (4/9)=-t/5
5ln(4/9)=-t
t=-5ln(4/9)
t=4.05 months